Coupling system to a microsphere cavity

ABSTRACT

A system of coupling optical energy in a waveguide mode, into a resonator that operates in a whispering gallery mode. A first part of the operation uses a fiber in its waveguide mode to couple information into a resonator e.g. a microsphere. The fiber is cleaved at an angle Φ which causes total internal reflection within the fiber. The energy in the fiber then forms an evanescent field and a microsphere is placed in the area of the evanescent field. If the microsphere resonance is resonant with energy in the fiber, then the information in the fiber is effectively transferred to the microsphere.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This is a divisional of U.S. application Ser. No. 09/501,824filed Feb. 10, 2000, which claims benefit of U.S. application Ser. No.60/119,435, filed Feb. 10, 1999 and U.S. application Ser. No. 60/123,696filed Mar. 8, 1999.

STATEMENT AS TO FEDERALLY-SPONSORED RESEARCH

[0002] The invention described herein was made in the performance ofwork under a NASA contract, and is subject to the provisions of PublicLaw 96-517 (U.S.C. 202) in which the Contractor has elected to retaintitle.

BACKGROUND

[0003] Microsphere resonators have certain desirable characteristicsincluding exceptionally high quality (“Q”) factors, and smalldimensions. Optical systems often use microsphere resonators as abuilding block for fiber optic systems. However, it is often necessaryto couple optical energy from an optical fiber into the microspherecavity. The existing couplers often suffer from certain drawbacks.

SUMMARY

[0004] This application teaches new ways of launching energy into aresonator device such as a microsphere resonator.

[0005] A first way of doing this is by operating using a direct fibercoupling to a resonator, e.g. a microsphere using a hybrid of awaveguide and prism coupler formed on the fiber itself. Another aspectof the disclosure describes using a surface grating on the resonator ina way that disrupts the evanescent field to allow input and outputcoupling.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] These and other aspects will now be described in detail withrespect to the accompanying drawings, wherein:

[0007]FIG. 1 shows an angle polished fiber coupler system for coupling amicrosphere;

[0008]FIG. 2 shows a model of sphere radius verses fiber characteristic;

[0009]FIGS. 3A and 3B show single mode fibers and a resonator;

[0010]FIGS. 4A and 4B shown an embodiment using this waveguide towhispering mode technique for coupling between different waveguides;

[0011] FIGS. 5A-5D show an embodiment for forming the waveguides on achip and forming a resonator near the waveguides;

[0012] FIGS. 6A-6C show details of a system for doing this using opticalwaveguides;

[0013]FIG. 7 shows an embodiment of carrying out electro-opticalabsorption on a chip;

[0014]FIG. 8 shows an embodiment which couples light into a resonatorusing a surface grating; and

[0015] FIGS. 9A-9C shows steps of formation of a improved resonator.

DETAILED DESCRIPTION

[0016]FIG. 1 shows the basic schematic embodiment of a first fibercoupler system. A single mode fiber 100 has an end 110 which will beused to couple propagating light 112 into a resonator 120 which can be amicrosphere resonator. The single mode fiber 100 is formed with its endarea 110 having an angled portion 114. The angled portion 114 forms anangle ω=180−Φ with the direction of the axis of the fiber, as shown. Theangle w is controlled as described herein.

[0017] The light is coupled in the direction 112 and incident on theangled surface. Upon incidence, the light propagating inside the corecomes into contact with the angled region 114. The light undergoes totalinternal reflection and then forms an evanescent field around the fiberend 110. Effectively the light escapes the fiber in this way. Themicrosphere 120 is placed in the area of the evanescent field. Theenergy from the evanescent field is efficiently exchanged in a resonantmode of the microsphere. Effectively, therefore, the information isresonantly transitioned between the “waveguide” mode of the single modefiber and the whispering gallery mode in the microsphere.

[0018] The angle 101 is selected to satisfy a phase matchingrequirement. The angle is selected according to the relationshipΦ=arcsin(n_(sphere)/n_(fiber)). N_(fiber) represents the effectiverefractive index that describes the guided wave in the fiber coretruncation area 110. N_(sphere) represents the effective refractionindex that describes the azimuthal propagation of waveguide modes. Thesecan be considered as closed waves, undergoing total internal reflectionin the microsphere.

[0019] The linear dimensions of the angle-cut core area can match to thearea of evanescent field overlap. This allows the system to operatesimilarly to a prism coupler with illuminated collimation focusingobjects.

[0020] The effective refraction index can be used to define theazimuthal propagation of the waveguide modes near the surface of thesphere. These can be calculated based on asymptotic expressions forwaveguide mode frequencies ω_(lq), where n_(sphere)=cl/aω_(lq). L and qare respectively azimut and radial mode indexes, a is the radius of thesphere and c is the speed of light. Different indices can be calculatedand used to form a model.

[0021] More specifically, the effective index to describe the azimuthalpropagation of the WG modes can be calculated as n_(sphere)=cl/aω_(lq)on the basis of asymptotic expressions for WG mode “positions” asfollows:$\omega_{lq} = {\frac{nc}{a}\left\lbrack {v + {2^{{- 1}/3}\alpha_{q}v^{1/3}} - \frac{P}{\left( {n^{2} - 1} \right)^{1/2}} + {\left( {\frac{3}{10}2^{{- 2}/3}} \right)\alpha_{q}^{2}v^{{- 1}/3}} - {\frac{2^{{- 1}/3}{P\left( {n^{2} - {2{P^{2}/3}}} \right)}}{\left( {n^{2} - 1} \right)^{3/2}}\alpha_{q}v^{{- 2}/3}} + {O\left( v^{- 1} \right)}} \right\rbrack}$

[0022] Again, l, q are azimuthal and radial mode indices respectively; ais the sphere radius; c is the speed of light; n is the refraction indexof the sphere material (n=1.4440 (1.4469) for silica at the wavelengthλ=1550 nm (1300 nm)); P=n for TE_(lmq) modes and P=1/n for TM_(lmq)modes; V=1+½; and α_(q) —is the q-th root of the Airy function, Ai(−z),equal to 2.338, 4.088, 5.521 for q=1, 2, 3 respectively. Results ofcalculation of n_(sphere) (at both wavelengths 1550 nm and 1300 nm) forsilica spheres of different radii are given in FIG. 2. The calculationis made for three lowest radial order modes TE (TM)_(lmq), q=1,2,3.

[0023] Since the guided wave in the core no longer exists afterreflection, precise calculation of n_(fiber) is a non-trivial taskimplying the explicit computation of the evanescent field in thetrunctation area. However, as confirmed by the experiments below, aconsistent recipe for a functional coupler can be based on astraightforward approximation that assumes n_(fiber) equal to theeffective mode index in a regular fiber.

[0024] In a specific embodiment, the standard Corning SMF-28 fiber isused with the germanium-doped core of diameter 2a =8.3 μm and indexdifference of 0.36%. The material index of the core was n₁=1.4505; thematerial index of the cladding n₂=1.4453 at the wavelength λ=1550 nm,and correspondingly n₁=1.4535 and n₂=1.4483 at λ=1300 nm (Corning IncProduct Information sheet PI1036, 1998). As known from the theory ofstep-index fibers (see e.g. L. B. Jeunhomme, Single-Mode Fiber Optics(Marcel Dekker, N.Y., 1983)), propagation constant □ for the core-guidedmode can be approximated as follows:${\beta \approx {{kn}_{2}\left\lbrack {1 + {\Delta \left( \frac{v}{V} \right)}^{2}} \right\rbrack}},$

[0025] where k=2π/λ—is the free-space wave vector; Δ=(n₁−n₂)/n₂ —therelative index difference; v is the normalized transverse decayconstant; V=k n₂ a(2Δ)^(½)—the normalized frequency. Using standardsolution v(V) for the fundamental LP₀₁ mode of the fiber and theparameters of our fiber, the effective index relevant to thephase-matching condition is n_(fiber) β/k =1.4476 at 1550 nm andn_(fiber)=1.4509 at 1300 nm.

[0026] One exemplary model is shown in FIG. 2. In this model, differentresults of calculations are presented for different q values, at thefrequency and for different resonators of different characteristics.

[0027] Another issue comes from the way in which the fiber and the modesoperate after reflection from the truncation plane. After thisreflection, the guided wave in the fiber no longer exists. Precisecalculation of n_(fiber) becomes difficult. This value is assumed to beequal to the effective index n_(guide) of the guided wave and theregular fiber, although the precise value may be difficult to obtain.

[0028] The specific way in which the system is used is shown in FIG. 3Aand 3B. A close up view of the assembly has two fiber couplers 300, 310,each with cleaved ends as described herein. The polishing angles of thefibers are about 12.1 degrees and 13.3 degrees respectively or Φ=77.9°and 7.6°. A fused silica rod 320 supports the microsphere 322 at aradius 235 μm between two angled conical fiber couplers. The opticalinformation can be updated between the fibers, via the sphere.

[0029] The above has described one way of coupling optical energy intosuch a microsphere. Since evanescent waves are used for the energycoupling, this is effectively near-field coupling.

[0030] The principle implemented in the above description of a singlemode optical fiber coupler can also be extended to use integrated opticwaveguides.

[0031]FIG. 4A shows a total internal reflection mirror on a channelwaveguide that provides a phase-matched excitation coupler for WG modes.The cutting angle Φ is defined, as previously, from the effective indexof the guide and the effective index of azimuthal propagation of WG modein particular sphere. Because of the high index available with planarsemiconductor waveguides (n_(guide)=3.0−3.5), optimal coupling can beachieved with wide variety of cavity materials, by adjusting the angle Φin accordance with the relation Φ=arcsin(n_(sphere)/n_(guide)).

[0032] For example, if InP waveguides having an n=3.17 are on an InGaAsPsupporting layer (n=3.50) over an InP substrate, the effective index for3 μm×3 μm cross section will be n_(guide=)3.30. The optimal angle forexcitation of TE_(lml) whispering gallery modes in 200 μm diameter fusedsilica sphere Φ=25°, all near the wavelength 1550 nm. The configurationdepicted in FIG. 6 can be fabricated by CVD (chemical vapor deposition)methods, lithography, wet etching, and subsequent cleaving of the waferto provide a flat mirror surface at the reflection plane. Moreconsistent results may be obtained with ion-assisted etching, or “IAE”.If only input coupling is required, the waveguide may be simplytruncated as shown in FIG. 4B at the cleave. No folded mirror isnecessary, even though that could further simplify the fabrication.Although configuration of the optical field may be disturbed because ofmode transformation in the truncation area, the phase-matched couplingcan still be achieved, with adjustment or experimental trimming of thetruncation angle.

[0033] A corner reflector, or truncated guide can be formed on the edgeof a substrate as shown in FIG. 4A. The throughput configuration, whichis the analog of FIG. 3B, can be achieved by assembling two chips at500, 502. The sides of a microsphere 504 can be arranged as shown inFIGS. 5A and 5B. Alternatively, the couplers can be formed in thecentral part of the chip 510, next to a through hole or a micromachineddepression 512 that will house a microcavity 504 as shown in FIG. 5C.

[0034] In any of FIGS. 5A-5C, the sphere 504 is arranged relative to thechip 500 as shown in FIG. 5D. Preferably the central diameter line ofthe sphere 500 is at or around the chip surface. This can facilitateholding the chip into place.

[0035]FIG. 5 shows the embodiments incorporating a microsphere cavity.The described method of coupling is applicable to all types of waveguidemode cavities **(including disks, rings etc.). It also provides a toolto achieve efficient coupling between integrated optics components ofdifferent materials and substrates.

[0036]FIG. 6 shows a filter element including a waveguide microcavitywithin a case collinear input and output fibers/waveguides 605, 610using a sphere for filtering non-resonant paths.

[0037]FIG. 6 shows an embodiment of device integration of a novelwaveguide coupler element for waveguide modes in microspheres. A coupledoptoelectronic oscillator (COEO) is based on a high-Q microsphere. COEOis a variant of a microwave optoelectronic oscillator, OEO (X.S.Yao, L.Maleki, JOSA B, Vol.13, No.8, pp.1725-35, 1996), which is a microwaveoscillator that uses optical energy storage elements to achieve highspectral purity signals at frequencies ranging from hundreds of MHz toabove 100 GHz. These devices, normally have a laser, optical modulator,detector, microwave amplifier and fiber-optic delay, optoelectronicoscillator. Each of these devices can be implemented on a single chipexcept for the relatively bulky delay element. By using a miniatureoptical cavity such as a microsphere, the entire device can be placed ona chip.

[0038] The waveguide coupling element described herein facilitates theincorporation of a microsphere in the OEO-on-chip, thereby simplifyingthe setup. To operate with an optical cavity, the laser in the OEOrequires locking to one of the modes of the cavity. Oscillation willoccur as the microwave modulation sidebands coincide with adjacentcavity modes.

[0039] To eliminate the need for independent laser locking to cavitymodes, the high-Q cavity can be incorporated into the laser resonator.An additional modulation feedback loop will ensure microwaveoscillation. This is described in, “coupled OEO,” (X. S. Yao, L. Maleki,Opt. Lett., Vol.22, No. 24, pp. 1867-9, 1997).

[0040] The embodiment of COEO-on-chip, is shown in FIG. 7. Whenactivated by a current source, the active waveguides 700, 702 providegain for the laser system. Electro-absorption modulators 705 arefabricated at the ends of waveguides by etching out the insulating gapto separate electrodes of gain sections from modulator sections. Theupper electroabsorption modulator is coated with a high-reflectivitycoating to induce pulse colliding in the modulator and thus enhance themode locking capability. At the lower section 702, the gap 710 betweenthe electroabsorption modulator and the waveguide is etched deeper toinduce optical separation. The gap interface acts as a partial mirror toreflect light back to the lower guide and form a laser cavity togetherwith high-Q microsphere and the upper waveguide terminated by a highreflectivity mirror. The lower electroabsorption modulator is reversebiased so that it acts as a photodetector. The output from thephotodetector is connected to the upper electroabsorption modulator viaa relatively simple matching circuit, to induce microwave oscillation.Because the photodetector and the E/A modulator are essentially the samedevice, they have similar impedances to the order of few K-Ohms. Thus,these devices are essentially impedance matched. Taking typical valuesof a 2 Volt modulator switching voltage, a 1 kOhm of modulator andphotodetector impedance, and 0.5 A/W of photodetector responsivity, theoptical power required for sustained RF oscillation can be estimated atonly 1.28 mW. Such an optical power is easily attainable insemiconductor lasers. This avoids the need for an RF amplifier, whichcan be a source of the proposed COEO design.

[0041] A second embodiment describes far field coupling, using arefractive index grating that is written onto the sphere surface. Thegrating can be written by shining a pattern of ultraviolet light onto adoped surface. The surface can be doped with germanium in order toincrease its photosensitivity.

[0042] The microsphere is formed as follows. First, a fused silicasphere is made in a typical way, such as by fusing a preform in a smallflame. A 3-5 μm thick photosensitive layer is then deposited by meltinggermanium oxide doped glass powder. The quality factor of the resultingsphere is about 10⁸ at λ=15-50 nanometers.

[0043] The photosensitive layer is then used to form a surface grating410 on the microsphere. 40 millowatts of a 244 nanometer UV light isused from a frequency-doubled argon laser for 5 to 10 minutes. Thisforms an index of modulation of about 10⁻⁴, with a grating period of 2μm and a grating length of about 15 μm. This grating will form firstorder phase matching of a whispering gallery mode and a free space beamthat is oriented at about 15 to 45° to the microsphere surface. Thecoupling of the optical information to the microsphere is shown in FIG.8. The microsphere 400 is also formed with surface grating 410.

[0044] A laser 420 produces laser light which is confined within awaveguide 422 that can be, for example, an optical fiber.

[0045] Collimating lens 424 receives optical energy from the waveguide.The optical energy is coupled to a prism 426. The prism can produce bothinput and output waves, the output wave being shown as 428. Light isalso coupled into the microsphere from the prism. The grating 410produces an output 430.

[0046] A technique of fabricating the cavity for a micro-sized resonatorsystem, capable of supporting whispering gallery modes, is alsodisclosed. This device can be used with any of the embodiments describedpreviously.

[0047] Silica microspheres can support whispering gallery modes based ontheir precise shaping and undercutting. A problem, however, is that manyof the microspheres with the highest quality have been hand-fabricatedin the laboratory.

[0048] The system herein forms a whispering gallery mode in a dielectricbody having axial symmetry e.g. a sphere, ellipsoid disk, ring or thelike. The microspheres that are described herein can actually be any ofthese shapes, or can be any other shaped resonator. This system can bemodeled by closed waves undergoing continuous total internal reflection.The resonances described herein correspond to completion of an integernumber of wavelengths packed along the closed trajectory.

[0049] The fabrication is shown with reference to FIGS. 9A-9C. Acylindrical cavity preform of silica is formed with vertical walls asshown in FIG. 9A. In this example, the walls have a diameter 100 to 200μm, a thickness of 20 to 40 μm, and are on a relatively flat substrate.

[0050] The vertical surface of the vertical walls is next re-shaped toprovide removal of the mode field from the flat boundaries as shown inFIG. 9B. This is done by removing the edge portions 900 forming acomplex shape shown in FIG. 9B. After that, further thermal andmechanical treatment is used to approach ellipsoidal geometry. Theedges, e.g. 510, are rounded and smoothed to minimize surface roughnessand reduce radiation loss. By rounding these surfaces, curvatureconfinement and fire polish grade surface can be obtained, obtaining a Qapproaching 10⁸.

[0051] The cylindrical preform described in FIG. 9A can be produced bywet/dry etch as well as ion milling techniques using appropriate crystalorientation. Other techniques such as RTA laser treatment, ultraviolettreatment and infrared treatment can also be used.

[0052] Other modifications are contemplated.

what is claimed is:
 1. A method comprising: forming a cylindrical cavitypreform with vertical walls; re-shaping said vertical walls in a waythat removes a mode field from flat boundaries of the vertical walls;treating the resulting shape to form an ellipsoidal geometry; androunding and smoothing edges of the ellipsoidal geometry to reduceradiation loss and to form a dielectric resonator body.
 2. A method asin claim 1 wherein said cylindrical cavity preform has walls with adiameter of 100 to 200 μm, and a thickness of 20 to 40 μm.
 3. A methodas in claim 1 wherein said treatment comprises one of wet/dry etching,ion milling techniques, RTA laser treatment, ultraviolet treatment orinfrared treatment.
 4. A method as in claim 1 wherein said preform isformed of a silica material.
 5. A resonator comprising a silica materialformed to have at least one substantially elliptical cross-sectionalarea.